We use two continuous-wave (CW) laser beams of 780 nm and 515 nm to optically
drive $^{85}$Rb atoms in a heated vapor cell to a low-lying Rydberg state
10D$_{5/2}$. We observe a collimated ultraviolet (UV) beam at 311 nm,
corresponding to the transition frequency from the 11P$_{3/2}$ state to the
5S$_{1/2}$ state. This indicates the presence of a coherent four-wave mixing
process, built up by two input laser fields as well as a terahertz (THz)
radiation of 3.28 THz that is generated by amplified spontaneous emission
between the 10D$_{5/2}$ and the 11P$_{3/2}$ states. We characterize the 311 nm
UV light generation and its dependence on various physical parameters. This
scheme could open up a new possibility for generating narrow-band THz waves as
well as deep UV radiation.

During multi-photon ionization of an atom it is well understood how the
involved photons transfer their energy to the ion and the photoelectron.
However, the transfer of the photon linear momentum is still not fully
understood. Here, we present a time-resolved measurement of linear momentum
transfer along the laser pulse propagation direction. Beyond the limit of the
electric dipole approximation we observe a time-dependent momentum transfer. We
can show that the time-averaged photon radiation pressure picture is not
generally applicable and the linear momentum transfer to the photoelectron
depends on the ionization time within the electromagnetic wave cycle using the
attoclock technique. We can mostly explain the measured linear momentum
transfer within a classical model for a free electron in a laser field.
However, corrections are required due to the interaction of the outgoing
photoelectron with the parent ion and due to the initial momentum when the
electron appears in the continuum. The parent ion interaction induces a
measurable negative attosecond time delay between the appearance in the
continuum of the electron with minimal linear momentum transfer and the point
in time with maximum ionization rate.

The phase of matter waves depends on proper time and is therefore susceptible
to special-relativistic (kinematic) and gravitational time dilation (redshift).
Hence, it is conceivable that atom interferometers measure general-relativistic
time-dilation effects. In contrast to this intuition, we show that light-pulse
interferometers without internal transitions are not sensitive to gravitational
time dilation, whereas they can constitute a quantum version of the
special-relativistic twin paradox. We propose an interferometer geometry
isolating the effect that can be used for quantum-clock interferometry.

Attosecond pulses in the soft-X-ray (SXR) to water-window energy region offer
the tools for creating and studying target specific localized inner-shell
electrons or holes in materials, enable monitoring or controlling charge and
energy flows in a dynamic system on attosecond timescales. Recently, a number
of laboratories have reported generation of continuum harmonics in the
hundred-electron-volt to kilovolt region with few-cycle long-wavelength
mid-infrared lasers. These harmonics have the bandwidth to support pulses with
duration of few- to few-ten attoseconds. But harmonics generated in a gas
medium have attochirps that cannot be fully compensated by materials over a
broad spectral range; thus, realistically what are the typical shortest
attosecond pulses that one can generate? To answer this question, it is
essential that the temporal attosecond pulses be accurately characterized. By
re-analyzing the soft X-ray harmonics reported in three recent experiments
\cite{chang_natcom2017,Thomas_OE2017,Bieger_2017PRX} using a newly developed
broadband phase retrieval algorithm, we show that their generated attosecond
pulses are all longer than about 60 as. Since broadband pulses tend to have
high-order chirps away from the spectral center of the pulse, the algorithm has
to be able to retrieve accurately the phase over the whole bandwidth. Our
re-evaluated pulse durations are found to be longer than those previously
reported. We also introduce the autocorrelation (AC) of the streaking
spectrogram. By comparing the ACs from the experiments and from the retrieved
SXR pulses, the accuracy of the retrieved results can be directly visualized to
ensure that correct phases have been obtained. Our retrieval method is fast and
accurate, and it shall provide a powerful tool for the metrology of
few-ten-attosecond pulses in the future.

Three-body recombination in quantum gases is traditionally associated with
heating, but it was recently found that it can also cool the gas. We show that
in a partially condensed three-dimensional homogeneous Bose gas three-body loss
could even purify the sample, that is, reduce the entropy per particle and
increase the condensed fraction $\eta$. We predict that the evolution of $\eta$
under continuous three-body loss can, depending on small changes in the initial
conditions, exhibit two qualitatively different behaviours - if it is initially
above a certain critical value, $\eta$ increases further, whereas clouds with
lower initial $\eta$ evolve towards a thermal gas. These dynamical effects
should be observable under realistic experimental conditions.